Document Type

Conference Proceeding

Publication Date

10-2012

Journal or Book Title

Proceedings of SPIE

Volume

8499

First Page

1

Last Page

14

DOI

10.1117/12.930862

Abstract

We propose a Bayesian expectation-maximization (EM) algorithm for reconstructing structured approximately sparse signals via belief propagation. The measurements follow an underdetermined linear model where the regression-coefficient vector is the sum of an unknown approximately sparse signal and a zero-mean white Gaussian noise with an unknown variance. The signal is composed of large- and small-magnitude components identified by binary state variables whose probabilistic dependence structure is described by a hidden Markov tree (HMT). Gaussian priors are assigned to the signal coefficients given their state variables and the Jeffreys’ noninformative prior is assigned to the noise variance. Our signal reconstruction scheme is based on an EM iteration that aims at maximizing the posterior distribution of the signal and its state variables given the noise variance. We employ a max-product algorithm to implement the maximization (M) step of our EM iteration. The noise variance is a regularization parameter that controls signal sparsity. We select the noise variance so that the corresponding estimated signal and state variables (obtained upon convergence of the EM iteration) have the largest marginal posterior distribution. Our numerical examples show that the proposed algorithm achieves better reconstruction performance compared with the state-of-the-art methods

Comments

This article is from Proceedings of SPIE 8499 (2012): 849908, doi:10.1117/12.930862. Posted with permission.

Rights

Copyright 2012 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.

Copyright Owner

Society of Photo-Optical Instrumentation Engineers

Language

en

File Format

application/pdf

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